2003/05/29 by Hiroshi Kori · 1 citation
Computer Science · Neuroscience · Physics and Astronomy · #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation #cond-mat.dis-nn #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreve.68.021919
11 pages, 8 figures, submitted to Phys. Rev. E
arxiv created 2003/05/29 · openalex publication_date 2003/08/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that peculiar collective dynamics called slow switching arises in a population of leaky integrate-and-fire oscillators with delayed, all-to-all pulse couplings. By considering the stability of cluster states and symmetry possessed by our model, we argue that saddle connections between a pair of the two-cluster states are formed under general conditions. Slow switching appears as a result of the system's approach to the saddle connections. It is also argued that such saddle connections are easy to arise near the bifurcation point where the state of perfect synchrony loses stability. We develop an asymptotic theory to reduce the model into a simpler form, with which an analytical study of the cluster states becomes possible.